450 Chapter 10 Data Displays Shapes of Distributions 10.3 How can you describe the shape of the distribution of a data set? Work with a partner. The lists at the left show the last four digits of a set of phone numbers in a phone book. a. Create a list that represents the last digit of each phone number shown. Make a dot plot of the data. b. In your own words, how would you describe the shape of the distribution? What single word do you think you can use to identify this type of distribution? Explain your reasoning. ACTIVITY: Describing the Shape of a Distribution 1 1 Work with a partner. The lists at the right show the first three digits of a set of phone numbers in a phone book. a. Create a list that represents the first digit of each phone number shown. Make a dot plot of the data. b. In your own words, how would you describe the shape of the distribution? What single word do you think you can use to identify this type of distribution? Explain your reasoning. c. In your dot plot, draw a vertical line through the middle of the data set. What do you notice? d. Repeat part (c) for the dot plot you constructed in Activity 1. What do you notice? Compare the distributions from Activities 1 and 2. ACTIVITY: Describing the Shape of a Distribution 2 2 Data Displays In this lesson, you will ● describe shapes of distributions.
Transcript
450 Chapter 10 Data Displays
Shapes of Distributions10.3
How can you describe the shape of the
distribution of a data set?
Work with a partner. The lists at the left show the last four digits of a set of phone numbers in a phone book.
a. Create a list that represents the last digit of each phone number shown. Make a dot plot of the data.
b. In your own words, how would you describe the shape of the distribution? What single word do you think you can use to identify this type of distribution? Explain your reasoning.
ACTIVITY: Describing the Shape of a Distribution11
Work with a partner. The lists at the right show the fi rst three digits of a set of phone numbers in a phone book.
a. Create a list that represents the fi rst digit of each phone number shown. Make a dot plot of the data.
b. In your own words, how would you describe the shape of the distribution? What single word do you think you can use to identify this type of distribution? Explain your reasoning.
c. In your dot plot, draw a vertical line through the middle of the data set. What do you notice?
d. Repeat part (c) for the dot plot you constructed in Activity 1. What do you notice? Compare the distributions from Activities 1 and 2.
ACTIVITY: Describing the Shape of a Distribution22
Data DisplaysIn this lesson, you will● describe shapes
5. IN YOUR OWN WORDS How can you describe the shape of the distribution of a data set?
6. Name two other ways you can describe the distribution of a data set.
Work with a partner. The table shows the Ages of Cellular Phones (years)
0 1 0 6 4
2 3 5 1 1
0 1 2 3 1
0 0 1 1 1
7 1 4 2 2
0 2 0 1 2
ages of cellular phones owned by a group of students.
a. Make a dot plot of the data.
b. In your own words, how would you describe the shape of the distribution? Compare it to the distributions in Activities 1 and 2.
c. Why do you think this type of distribution is called a skewed distribution?
ACTIVITY: Describing the Shape of a Distribution33
Work with a partner.
a. Find the means and the medians of the data sets in Activities 1−3.
b. What do you notice about the means and the medians of the data sets and the shapes of the distributions? Explain.
c. Which measure of center do you think best describes the data set in Activity 2? in Activity 3? Explain your reasoning.
d. Using your answers to part (c), decide which measure of variation you think best describes the data set in Activity 2. Which measure of variation do you think best describes the data set in Activity 3? Explain your reasoning.
ACTIVITY: Finding Measures of Center44
Use what you learned about shapes of distributions to complete Exercises 3 and 4 on page 454.
When something is skewed, it has a slanted direction or position.
Skewed
Use Prior ResultsHow is the distribution of the data related to the mean and the median?
EXAMPLE Describing the Shapes of Distributions11Describe the shape of each distribution.
a. b.
Most of the data are on the The left side of the graph isleft, and the tail extends to approximately a mirror imagethe right. of the right side of the graph.
So, the distribution So, the distribution is skewed right. is symmetric.
1. Describe the shape of the distribution.Exercises 5–8
You can use dot plots and histograms to identify shapes of distributions.
Symmetric and Skewed Distributions
Skewed left Symmetric Skewed right
● The “tail” of the graph extends to the left.
● The left side of the graph is a mirror image of the right side of the graph.
● The “tail” of the graph extends to the right.
● Most data are on the right.
● Most data are on the left.
tailtail
Study TipIf all the dots of a dot plot or bars of a histogram are about the same height, then the distribution is a fl at, or uniform, distribution. A uniform distribution is also symmetric.
The frequency table shows the ages of people watching a comedy in a theater. Display the data in a histogram. Describe the shape of the distribution.
Draw and label the axes. Then draw a bar to represent the frequency ofeach interval.
Most of the data are on the right, and the tail extends to the left.
So, the distribution is skewed left.
The histogram shows the ages of people watching an animated movie in the same theater as in Example 2.
a. Describe the shape of the distribution.
Most of the data are on the left, and the tail extends to the right.
So, the distribution is skewed right.
b. Which movie has an older audience?
The intervals in the histograms are the same. Most of the data for the animated movie are on the left, while most of the data for the comedy are on the right. This means that the people watching the comedy are generally older than the people watching the animated movie.
So, the comedy has an older audience.
2. The frequency table shows the ages of people watching a historical movie in a theater.
Ages 10−19 20−29 30−39 40−49 50−59 60−69
Frequency 3 18 36 40 14 5
a. Display the data in a histogram. Describe the shape of the distribution.
b. Compare the distribution of the data to the distributions in Examples 2 and 3. What can you conclude?
1. VOCABULARY How does the shape of a symmetric distribution differ from the shape of a skewed distribution?
2. VOCABULARY For a distribution that is skewed right, which direction does the tail extend? Where do most of the data lie?
9+(-6)=3
3+(-3)=
4+(-9)=
9+(-1)=
Make a dot plot of the data. In your own words, how would you describe the shape of the distribution?
3. Miles Run per Day
1 4 2 0 3 2 1 2 4 2 3
2 1 6 3 2 4 0 5 3 1 5
4. Raffl e Tickets Sold
15 12 16 15 13 14 16 13
13 16 14 12 15 12 14
Describe the shape of each distribution.
5.
25 26 27 2928 30
Number ofstudents
Class Sizes 6.
15 16 17 1918 2120
Height(inches)
Heights of Plants
7.
10
20
30
40
50
60
0–4
0
Minutes
Freq
uen
cy
Travel Time to School
5–9
10–1
4
15–1
9
20–2
4
25–2
9
8.
20
40
60
80
100
120
0
Age
Freq
uen
cy
Ages of People at a Concert
0–9
10–1
9
20–2
9
30–3
9
40–4
9
50–5
9
60–6
9
9. POLICE The frequency table shows the years of service for the police offi cers of Jones County and Pine County. Display the data for each county in a histogram. Describe the shape of each distribution. Which county’s police force has less experience? Explain.
Years of Service 0–3 4–7 8–11 12–15 16–19 20–23 24–27
17. MULTIPLE CHOICE Sixty people participate in a trivia contest. How many four-person teams can be formed? (Section 7.3)
○A 15 ○B 56 ○C 64 ○D 240
10. REASONING What is the shape of the distribution of the restaurant waiting times? Explain your reasoning.
11. LOGIC Are all distributions either approximately symmetric or skewed? Explain. If not, give an example.
12. REASONING Can you use a stem-and-leaf plot to describe the shape of a distribution? Explain your reasoning.
13. CHARITY The table shows the donation amounts received by a charity in one day.
Donations (dollars)
20 15 40 70 20 5 25 50 47 20 62 55 40
10 50 18 20 100 40 80 60 20 80 3 30 50
25 30 10 33 20 50 7 35 40 25 70
a. Make a histogram of the data starting with the interval 0–14. Describe the shape of the distribution.
b. A company adds $5 to each donation. Make another histogram starting with the same fi rst interval as in part (a). Compare the shape of this distribution with the distribution in part (a). Explain any differences in the distributions.
14. Describe the shape of the distribution of each bar graph. Match the letters A, B, and C with the mean, the median, and the mode of the data set. Explain your reasoning.
![Modeling Deformable Objects from a Single Depth Cameravigir.missouri.edu/~gdesouza/Research/Conference... · ing a combination of several basic shapes [1, 3], Gaussian distributions](https://static.documents.pub/doc/80x56/5fbfdfa553b14258c2000b69/modeling-deformable-objects-from-a-single-depth-gdesouzaresearchconference.jpg)
